This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.
We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac{A \cdot STDAGE_{t2}}{k+STDAGE_{t2}}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the peak growing season (June-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1960-1989), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Model selection is used to determine the best fitting models, which is implemented in two parts. The first part selected the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).
model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
model 3: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
sub-model b: s form \(\left( \frac {A \cdot STDAGE_{t2}^s} {k^s+STDAGE_{t2}^s} \right)\)
sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot STDAGE_{t2}^s} {k^s + STDAGE_{t1}^s} \right)\)
Note:
This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval
This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):
Below the model fitting procedure is implemented by ecoprovince:
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6803 1682.7
## 2 6802 1681.9 1 0.817 3.3024 0.06922 .
## 3 6801 1508.3 1 173.521 782.3941 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 73664.85
## 2 2 73663.54
## 3 3 72924.43
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.224e-01 1.983e-01 2.13 0.0332 *
## phi 9.657e-03 6.353e-03 1.52 0.1286
## alpha 8.551e-01 2.782e-02 30.73 <2e-16 ***
## A 4.130e+02 2.663e+01 15.51 <2e-16 ***
## k 1.748e+02 1.210e+01 14.44 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4709 on 6801 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.741e-06
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6801 1508.3
## 2 6800 1507.4 1 0.96192 4.3394 0.03728 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 72924.43
## 2 3a 72922.09
## 3 3b NA
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.372e-01 1.995e-01 2.192 0.0284 *
## phi 9.948e-03 6.376e-03 1.560 0.1188
## alpha 8.524e-01 2.770e-02 30.769 < 2e-16 ***
## A 4.689e+02 5.544e+01 8.458 < 2e-16 ***
## k 2.195e+02 3.752e+01 5.849 5.16e-09 ***
## p 1.022e-02 4.649e-03 2.198 0.0280 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4708 on 6800 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 8.162e-06
## Warning: Removed 292 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 292 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 67 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18749 6338.2
## 2 18744 6337.9 5 0.261 0.1545 0.9787
## 3 18743 6070.3 1 267.554 826.1114 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 195514.5
## 2 2 195475.2
## 3 3 194668.6
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.353588 0.110897 3.188 0.00143 **
## phi -0.001996 0.003688 -0.541 0.58844
## alpha 0.737003 0.023797 30.971 < 2e-16 ***
## A 179.312279 5.156726 34.773 < 2e-16 ***
## k 69.228552 2.165126 31.974 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5691 on 18743 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.228e-06
## (27 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18743 6070.3
## 2 18742 6024.5 1 45.811 142.52 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 194668.6
## 2 3a 194528.5
## 3 3b 194664.1
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.306503 0.108473 2.826 0.00472 **
## phi -0.001440 0.003674 -0.392 0.69515
## alpha 0.721462 0.021813 33.074 < 2e-16 ***
## A 220.082506 9.814957 22.423 < 2e-16 ***
## k 112.272660 7.835130 14.329 < 2e-16 ***
## p 0.039500 0.002695 14.655 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.567 on 18742 degrees of freedom
##
## Number of iterations to convergence: 14
## Achieved convergence tolerance: 7.397e-06
## (27 observations deleted due to missingness)
## Warning: Removed 709 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 709 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 140 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7166 1248.9
## 2 7165 1248.8 1 0.09 0.5136 0.4736
## 3 7156 1115.0 9 133.80 95.4108 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 78262.17
## 2 2 78263.66
## 3 3 77388.99
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.177767 0.125695 1.414 0.157
## phi -0.003182 0.004610 -0.690 0.490
## alpha 0.833125 0.026621 31.295 <2e-16 ***
## A 471.875581 24.383587 19.352 <2e-16 ***
## k 142.228754 8.530248 16.673 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3947 on 7156 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.873e-06
## (9 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7156 1115.0
## 2 7155 1114.7 1 0.32532 2.0881 0.1485
## model AIC
## 1 3 77388.99
## 2 3a 77388.90
## 3 3b 77366.35
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.230108 0.128881 1.785 0.0742 .
## phi -0.003611 0.004596 -0.786 0.4321
## alpha 0.841062 0.026798 31.385 <2e-16 ***
## A 307.335491 21.963531 13.993 <2e-16 ***
## k 68.630153 7.052532 9.731 <2e-16 ***
## s 1.252251 0.052561 23.825 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3941 on 7155 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.799e-06
## (9 observations deleted due to missingness)
## Warning: Removed 214 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 214 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 95 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4870 1492.4
## 2 4869 1491.8 1 0.593 1.9356 0.1642
## 3 4862 1388.0 7 103.773 51.9275 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 52508.96
## 2 2 52509.02
## 3 3 52116.67
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.108312 0.201218 -0.538 0.590
## phi 0.021351 0.009589 2.227 0.026 *
## alpha 0.875306 0.042046 20.818 <2e-16 ***
## A 450.989851 38.681653 11.659 <2e-16 ***
## k 187.931256 18.156596 10.351 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5343 on 4862 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 6.47e-06
## (10 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4862 1388.0
## 2 4861 1386.8 1 1.2116 4.2469 0.03938 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 52116.67
## 2 3a 52114.42
## 3 3b NA
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.086726 0.203625 -0.426 0.6702
## phi 0.021015 0.009581 2.193 0.0283 *
## alpha 0.885443 0.042244 20.960 < 2e-16 ***
## A 396.339480 42.136289 9.406 < 2e-16 ***
## k 150.640293 23.061134 6.532 7.14e-11 ***
## p -0.011878 0.007526 -1.578 0.1145
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5341 on 4861 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 5.24e-06
## (10 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95924, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -31.565, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 160 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 160 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 57 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8773 1635.6
## 2 8772 1634.2 1 1.345 7.2189 0.007228 **
## 3 8768 1511.6 4 122.662 177.8789 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 92156.63
## 2 2 92151.41
## 3 3 91445.87
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.211037 0.117857 1.791 0.07339 .
## phi -0.015961 0.005137 -3.107 0.00189 **
## alpha 0.776341 0.027255 28.484 < 2e-16 ***
## A 246.896440 9.049774 27.282 < 2e-16 ***
## k 72.053158 3.462078 20.812 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4152 on 8768 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.748e-06
## (10 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8768 1511.6
## 2 8767 1511.5 1 0.028753 0.1668 0.683
## model AIC
## 1 3 91445.87
## 2 3a 91447.70
## 3 3b 91417.00
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.222553 0.118311 1.881 0.05999 .
## phi -0.015283 0.005127 -2.981 0.00288 **
## alpha 0.780966 0.027354 28.550 < 2e-16 ***
## A 181.122164 8.521131 21.256 < 2e-16 ***
## k 40.816766 2.670898 15.282 < 2e-16 ***
## s 1.356136 0.063516 21.351 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4145 on 8767 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.465e-06
## (10 observations deleted due to missingness)
## Warning: Removed 275 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 275 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 44 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12328 3402.9
## 2 12327 3401.7 1 1.174 4.2556 0.03914 *
## 3 12326 3168.4 1 233.379 907.9214 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 134092.1
## 2 2 134089.8
## 3 3 133215.4
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.352889 0.136159 9.936 <2e-16 ***
## phi -0.009457 0.004513 -2.096 0.0361 *
## alpha 0.625058 0.019024 32.855 <2e-16 ***
## A 228.475174 7.054443 32.387 <2e-16 ***
## k 54.645649 1.681040 32.507 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.507 on 12326 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.105e-06
## (16 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12326 3168.4
## 2 12325 3071.9 1 96.516 387.24 < 2.2e-16 ***
## 3 12325 3133.0 0 0.000
## 4 12324 2996.0 1 137.008 563.58 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 133215.4
## 2 3a 132836.0
## 3 3b 133079.1
## 4 3c 132529.7
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.823084 0.153940 11.843 < 2e-16 ***
## phi -0.012617 0.004372 -2.886 0.00391 **
## alpha 0.724875 0.014206 51.027 < 2e-16 ***
## A 136.610805 4.469965 30.562 < 2e-16 ***
## k 32.316058 0.886557 36.451 < 2e-16 ***
## p 0.176183 0.007462 23.610 < 2e-16 ***
## s 2.205140 0.091515 24.096 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4931 on 12324 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 8.858e-06
## (16 observations deleted due to missingness)
## Warning: Removed 382 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 382 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 68 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12427 5120.9
## 2 12426 5118.1 1 2.827 6.8637 0.008807 **
## 3 12425 4833.3 1 284.863 732.3053 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 138056.4
## 2 2 138051.6
## 3 3 137341.7
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 8.572e-01 1.436e-01 5.969 2.45e-09 ***
## phi 1.414e-02 5.721e-03 2.472 0.0135 *
## alpha 6.367e-01 2.131e-02 29.881 < 2e-16 ***
## A 2.328e+02 8.568e+00 27.167 < 2e-16 ***
## k 5.338e+01 2.004e+00 26.642 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6237 on 12425 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.379e-06
## (40 observations deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_232, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12425 4833.3
## 2 12424 4689.0 1 144.248 382.20 < 2.2e-16 ***
## 3 12423 4615.3 1 73.722 198.44 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 137341.7
## 2 3a 136967.1
## 3 3b NA
## 4 3c 136772.1
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.090e+00 1.503e-01 7.253 4.31e-13 ***
## phi 1.466e-02 5.562e-03 2.636 0.00839 **
## alpha 7.472e-01 1.529e-02 48.872 < 2e-16 ***
## A 1.517e+02 5.942e+00 25.527 < 2e-16 ***
## k 3.507e+01 1.268e+00 27.655 < 2e-16 ***
## p 1.838e-01 9.439e-03 19.475 < 2e-16 ***
## s 2.151e+00 1.096e-01 19.632 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6095 on 12423 degrees of freedom
##
## Number of iterations to convergence: 18
## Achieved convergence tolerance: 6.557e-06
## (40 observations deleted due to missingness)
## Warning: Removed 459 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 459 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 84 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1260 341.40
## 2 1259 340.98 1 0.414 1.5275 0.2167
## 3 1258 304.55 1 36.436 150.5075 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 14064.19
## 2 2 14064.66
## 3 3 13923.93
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.03235 0.38674 -0.084 0.933
## phi 0.02239 0.01919 1.167 0.243
## alpha 0.76482 0.05648 13.542 < 2e-16 ***
## A 534.76505 90.58922 5.903 4.58e-09 ***
## k 150.62413 29.17636 5.163 2.83e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.492 on 1258 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 6.796e-06
## (2 observations deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1258 304.55
## 2 1257 303.96 1 0.58527 2.4203 0.12
## model AIC
## 1 3 13923.93
## 2 3a 13923.50
## 3 3b NA
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.068800 0.379721 -0.181 0.85625
## phi 0.024165 0.019198 1.259 0.20837
## alpha 0.756814 0.056010 13.512 < 2e-16 ***
## A 914.887761 480.230226 1.905 0.05699 .
## k 324.181993 213.143210 1.521 0.12852
## p 0.012477 0.004042 3.087 0.00207 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4917 on 1257 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.186e-06
## (2 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96021, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -11.162, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 34 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 34 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 29 row(s) containing missing values (geom_path).
## Error in nls(f_1, data = G_242, start = c(ge = ge.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(f_2, data = G_242, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## Error in nls(f_3, data = G_242, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1793 399.39
## 2 1792 399.38 1 0.0056 0.0253 0.8737
## 3 1791 377.43 1 21.9521 104.1677 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18766.17
## 2 2 18768.15
## 3 3 18668.61
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.208773 0.327252 0.638 0.524
## phi -0.003168 0.012502 -0.253 0.800
## alpha 0.750699 0.068278 10.995 <2e-16 ***
## A 277.874870 28.834628 9.637 <2e-16 ***
## k 106.568383 12.736078 8.367 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4591 on 1791 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 5.734e-06
## (1 observation deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1791 377.43
## 2 1790 376.81 1 0.62625 2.975 0.08473 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 18668.61
## 2 3a 18667.63
## 3 3b 18645.17
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.23065 0.32840 0.702 0.483
## phi -0.00104 0.01255 -0.083 0.934
## alpha 0.76426 0.06853 11.153 <2e-16 ***
## A 149.64370 13.42374 11.148 <2e-16 ***
## k 38.36509 3.00470 12.768 <2e-16 ***
## s 1.82807 0.16802 10.880 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4559 on 1790 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.976e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96947, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -18.321, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 60 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 60 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 55 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 658 209.60
## 2 657 209.57 1 0.023 0.072 0.7885
## 3 656 190.82 1 18.755 64.477 4.528e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6702.388
## 2 2 6704.315
## 3 3 6644.344
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.09785 0.39859 -0.245 0.806
## phi -0.04344 0.02679 -1.622 0.105
## alpha 0.77374 0.08594 9.003 < 2e-16 ***
## A 191.05053 26.63609 7.173 1.99e-12 ***
## k 54.86848 9.52757 5.759 1.30e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5393 on 656 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.699e-06
## (2 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 656 190.82
## 2 655 190.80 1 0.018429 0.0633 0.8015
## model AIC
## 1 3 6644.344
## 2 3a 6646.280
## 3 3b 6640.117
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.15197 0.38750 -0.392 0.6951
## phi -0.04738 0.02660 -1.781 0.0754 .
## alpha 0.80479 0.08649 9.305 < 2e-16 ***
## A 122.71846 16.14074 7.603 1.01e-13 ***
## k 23.86754 3.54344 6.736 3.57e-11 ***
## s 1.65406 0.24745 6.685 4.96e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5372 on 655 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 7.623e-06
## (2 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94016, p-value = 1.183e-15
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -9.6852, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 20 3.4359
## 2 19 3.4302 1 0.005736 0.0318 0.8604
## 3 18 3.1869 1 0.243212 1.3737 0.2565
## model AIC
## 1 1 308.6562
## 2 2 310.6177
## 3 3 310.9262
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -2.726 0.354 -7.701 2.09e-07 ***
## A 8572.749 9212.429 0.931 0.363
## k 717.133 829.205 0.865 0.397
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4145 on 20 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 9.519e-07
## (1 observation deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 20 3.4359
## 2 19 3.4358 1 5.6057e-05 3e-04 0.9861
## model AIC
## 1 1 308.6562
## 2 1a 310.6558
## 3 1b 310.6552
## 4 1c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -2.726 0.354 -7.701 2.09e-07 ***
## A 8572.749 9212.429 0.931 0.363
## k 717.133 829.205 0.865 0.397
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4145 on 20 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 9.519e-07
## (1 observation deleted due to missingness)
add p model: fits
add s model: fits
add s+p model: does not fit
unable to fit model (only 64 observations)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96671, p-value = 0.6107
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 1.1715, p-value = 0.2414
## alternative hypothesis: two.sided
## Warning: Removed 2 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 2 rows containing missing values (geom_segment).
## Warning: Removed 275 row(s) containing missing values (geom_path).
## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 2 rows containing missing values (geom_segment).
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_262.' not found
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 151 26.657
## 2 150 26.628 1 0.02844 0.1602 0.6895331
## 3 149 24.403 1 2.22523 13.5869 0.0003183 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1931.239
## 2 2 1933.074
## 3 3 1921.635
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.45026 1.56137 0.288 0.773458
## phi -0.03686 0.06427 -0.573 0.567172
## alpha 0.90066 0.22752 3.959 0.000116 ***
## A 1723.50465 754.16358 2.285 0.023705 *
## k 330.70576 96.49416 3.427 0.000788 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4047 on 149 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.76e-06
## (1 observation deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_263, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 149 24.403
## 2 148 24.330 1 0.073144 0.4449 0.5058
## model AIC
## 1 3 1921.635
## 2 3a 1923.173
## 3 3b 1923.633
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.45026 1.56137 0.288 0.773458
## phi -0.03686 0.06427 -0.573 0.567172
## alpha 0.90066 0.22752 3.959 0.000116 ***
## A 1723.50465 754.16358 2.285 0.023705 *
## k 330.70576 96.49416 3.427 0.000788 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4047 on 149 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.76e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9769, p-value = 0.01083
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.8959, p-value = 0.05798
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 211 66.388
## 2 210 66.383 1 0.005176 0.0164 0.8983
## 3 209 66.150 1 0.232699 0.7352 0.3922
## model AIC
## 1 1 2297.872
## 2 2 2299.855
## 3 3 2301.104
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.9053 0.9254 -0.978 0.3291
## A 293.7335 118.6877 2.475 0.0141 *
## k 168.8293 74.2410 2.274 0.0240 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5609 on 211 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 3.537e-06
## (1 observation deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 211 66.388
## 2 210 66.366 1 0.021814 0.069 0.793
## model AIC
## 1 1 2297.872
## 2 1a 2299.801
## 3 1b NA
## 4 1c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.9053 0.9254 -0.978 0.3291
## A 293.7335 118.6877 2.475 0.0141 *
## k 168.8293 74.2410 2.274 0.0240 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5609 on 211 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 3.537e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91405, p-value = 8.398e-10
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.328, p-value = 0.1842
## alternative hypothesis: two.sided
## Warning: Removed 8 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 8 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 81 row(s) containing missing values (geom_path).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Error in nls(f_1, data = G_322, start = c(ge = ge.start, A = A.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 300 169.49
## 2 299 157.71 1 11.7794 22.3326 3.534e-06 ***
## 3 298 155.97 1 1.7346 3.3141 0.06969 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3097.199
## 2 2 3077.373
## 3 3 3076.022
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 5.57640 6.13672 0.909 0.3642
## phi -0.11573 0.02054 -5.633 4.09e-08 ***
## alpha 0.46057 0.24332 1.893 0.0593 .
## A 35.68667 22.88602 1.559 0.1200
## k 23.38590 9.59842 2.436 0.0154 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7235 on 298 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 7.166e-06
## (1 observation deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_331, :
## parameters without starting value in 'data': ge
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_331, :
## parameters without starting value in 'data': ge
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_331, :
## parameters without starting value in 'data': ge
## model AIC
## 1 3 3076.022
## 2 3a NA
## 3 3b NA
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 5.57640 6.13672 0.909 0.3642
## phi -0.11573 0.02054 -5.633 4.09e-08 ***
## alpha 0.46057 0.24332 1.893 0.0593 .
## A 35.68667 22.88602 1.559 0.1200
## k 23.38590 9.59842 2.436 0.0154 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7235 on 298 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 7.166e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90559, p-value = 7.773e-13
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.4891, p-value = 7.152e-06
## alternative hypothesis: two.sided
* Cannot fit model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 191 97.286
## 2 190 97.242 1 0.04356 0.0851 0.77079
## 3 189 94.642 1 2.60066 5.1935 0.02379 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2085.408
## 2 2 2087.321
## 3 3 2084.062
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.35442 1.80312 0.197 0.8444
## phi 0.01096 0.05265 0.208 0.8353
## alpha 0.73232 0.29037 2.522 0.0125 *
## A 280.40101 204.47827 1.371 0.1719
## k 166.97985 140.70361 1.187 0.2368
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7076 on 189 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.702e-06
## (1 observation deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 189 94.642
## 2 187 92.984 2 1.6575 1.6666 0.1917
## model AIC
## 1 3 2084.062
## 2 3a NA
## 3 3b NA
## 4 3c 2084.635
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.35442 1.80312 0.197 0.8444
## phi 0.01096 0.05265 0.208 0.8353
## alpha 0.73232 0.29037 2.522 0.0125 *
## A 280.40101 204.47827 1.371 0.1719
## k 166.97985 140.70361 1.187 0.2368
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7076 on 189 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.702e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.87017, p-value = 7.517e-12
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.5075, p-value = 3.639e-08
## alternative hypothesis: two.sided
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 117 78.061
## 2 116 77.624 1 0.4369 0.6529 0.4207
## 3 109 73.777 7 3.8472 0.8120 0.5792
## model AIC
## 1 1 1267.796
## 2 2 1269.123
## 3 3 1207.774
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.63609 1.22318 -1.338 0.1838
## phi -0.01838 0.08470 -0.217 0.8286
## alpha 0.63289 0.27137 2.332 0.0215 *
## A 81.82085 45.34337 1.804 0.0739 .
## k -1.29940 1.48439 -0.875 0.3833
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8227 on 109 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 9.54e-06
## (7 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 109 73.777
## 2 108 71.574 1 2.2026 3.3235 0.07106 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 1207.774
## 2 3a 1206.318
## 3 3b NA
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.052537 1.909452 -0.551 0.583
## phi -0.009892 0.082404 -0.120 0.905
## alpha 0.559295 0.288286 1.940 0.055 .
## A 68.811869 46.891349 1.467 0.145
## k -8.039455 1.320643 -6.088 1.78e-08 ***
## p 1.218451 0.143912 8.467 1.38e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8141 on 108 degrees of freedom
##
## Number of iterations to convergence: 20
## Achieved convergence tolerance: 3.644e-06
## (7 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90381, p-value = 5.439e-07
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.1984, p-value = 0.2308
## alternative hypothesis: two.sided
## Warning: Removed 4 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 81 row(s) containing missing values (geom_path).
## Error in nls(f_1, data = G_411, start = c(ge = ge.start, A = A.start, :
## singular gradient
## Error in nls(f_2, data = G_411, start = c(ge = ge.start, phi = phi.start, :
## singular gradient
## Error in nls(f_3, data = G_411, start = c(ge = ge.start, phi = phi.start, :
## singular gradient
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_411$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_411.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6723 1277.2
## 2 6722 1270.9 1 6.306 33.355 8.021e-09 ***
## 3 6721 1093.8 1 177.024 1087.705 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 71147.96
## 2 2 71116.66
## 3 3 70109.75
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.631e-01 1.559e-01 2.971 0.00298 **
## phi 2.684e-02 5.634e-03 4.764 1.94e-06 ***
## alpha 8.139e-01 2.240e-02 36.331 < 2e-16 ***
## A 4.026e+02 2.188e+01 18.401 < 2e-16 ***
## k 1.738e+02 9.865e+00 17.616 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4034 on 6721 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.565e-06
## (3 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6721 1093.8
## 2 6720 1089.7 1 4.1771 25.76 3.97e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 70109.75
## 2 3a 70086.01
## 3 3b 70071.49
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s +
## STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.009e-01 1.514e-01 2.647 0.00814 **
## phi 2.559e-02 5.598e-03 4.571 4.95e-06 ***
## alpha 8.209e-01 2.250e-02 36.484 < 2e-16 ***
## A 2.448e+02 1.610e+01 15.206 < 2e-16 ***
## k 7.243e+01 6.842e+00 10.586 < 2e-16 ***
## s 1.285e+00 4.927e-02 26.085 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4022 on 6720 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 6.91e-06
## (3 observations deleted due to missingness)
## Warning: Removed 239 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 239 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 105 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8029 1308.9
## 2 8028 1293.3 1 15.649 97.144 < 2.2e-16 ***
## 3 8027 1209.8 1 83.468 553.804 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 88720.87
## 2 2 88626.26
## 3 3 88092.39
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.94893 0.12701 7.471 8.78e-14 ***
## phi -0.04165 0.00415 -10.035 < 2e-16 ***
## alpha 0.84742 0.03405 24.887 < 2e-16 ***
## A 247.98550 7.87553 31.488 < 2e-16 ***
## k 56.74056 2.30892 24.575 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3882 on 8027 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.567e-06
## (2 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8027 1209.8
## 2 8026 1209.8 1 0.0293 0.1946 0.6591
## 3 8026 1203.1 0 0.0000
## 4 8025 1176.4 1 26.6548 181.8236 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 88092.39
## 2 3a 88094.20
## 3 3b 88049.73
## 4 3c 87871.78
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.105617 0.132922 8.318 <2e-16 ***
## phi -0.040438 0.004079 -9.915 <2e-16 ***
## alpha 0.845599 0.031498 26.846 <2e-16 ***
## A 155.445661 4.473193 34.750 <2e-16 ***
## k 38.721092 0.820010 47.220 <2e-16 ***
## p 0.256607 0.014195 18.077 <2e-16 ***
## s 2.984550 0.182924 16.316 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3829 on 8025 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 9.026e-06
## (2 observations deleted due to missingness)
## Warning: Removed 281 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 281 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 55 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 879 117.885
## 2 878 114.794 1 3.0906 23.638 1.377e-06 ***
## 3 877 99.686 1 15.1085 132.919 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8959.561
## 2 2 8938.129
## 3 3 8815.663
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.59246 0.22382 -2.647 0.00827 **
## phi 0.07663 0.01799 4.260 2.27e-05 ***
## alpha 0.89078 0.07113 12.523 < 2e-16 ***
## A 313.66069 35.61950 8.806 < 2e-16 ***
## k 90.94404 14.60378 6.227 7.35e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3371 on 877 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.364e-07
## (1 observation deleted due to missingness)
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 877 99.686
## 2 876 99.627 1 0.05894 0.5182 0.4718
## model AIC
## 1 3 8815.663
## 2 3a 8817.141
## 3 3b 8817.619
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.59246 0.22382 -2.647 0.00827 **
## phi 0.07663 0.01799 4.260 2.27e-05 ***
## alpha 0.89078 0.07113 12.523 < 2e-16 ***
## A 313.66069 35.61950 8.806 < 2e-16 ***
## k 90.94404 14.60378 6.227 7.35e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3371 on 877 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.364e-07
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96684, p-value = 2.824e-13
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.825, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 12 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 12 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 20 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 984 217.32
## 2 983 217.06 1 0.2618 1.1857 0.2765
## 3 982 201.70 1 15.3596 74.7812 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 10199.92
## 2 2 10200.73
## 3 3 10130.29
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 5.339e-01 5.387e-01 0.991 0.322
## phi 7.847e-03 2.238e-02 0.351 0.726
## alpha 7.571e-01 8.138e-02 9.303 < 2e-16 ***
## A 2.705e+02 4.192e+01 6.454 1.71e-10 ***
## k 1.134e+02 1.838e+01 6.171 9.94e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4532 on 982 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.112e-06
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 982 201.70
## 2 981 201.22 1 0.47469 2.3142 0.1285
## 3 981 201.36 0 0.00000
## 4 980 201.13 1 0.22138 1.0786 0.2993
## model AIC
## 1 3 10130.29
## 2 3a 10129.97
## 3 3b 10130.62
## 4 3c 10131.54
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.48861 0.52896 0.924 0.35586
## phi 0.00759 0.02242 0.338 0.73507
## alpha 0.75459 0.07890 9.563 < 2e-16 ***
## A 367.93804 120.22982 3.060 0.00227 **
## k 188.46256 85.11530 2.214 0.02704 *
## p 0.01754 0.00731 2.399 0.01661 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4529 on 981 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.461e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96238, p-value = 2.899e-15
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.314, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 25 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 25 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 33 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3174 1936.4
## 2 3173 1936.2 1 0.271 0.4434 0.5055
## 3 3150 1809.7 23 126.501 9.5737 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 42013.68
## 2 2 42015.23
## 3 3 41577.57
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -2.300e-01 4.840e-01 -0.475 0.635
## phi -1.041e-03 1.522e-02 -0.068 0.945
## alpha 1.073e+00 6.863e-02 15.633 < 2e-16 ***
## A 1.031e+03 1.551e+02 6.644 3.59e-11 ***
## k 2.895e+02 2.633e+01 10.996 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.758 on 3150 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.361e-06
## (24 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3150 1809.7
## 2 3149 1793.2 1 16.4951 28.9671 7.901e-08 ***
## 3 3148 1791.5 1 1.6379 2.8781 0.08989 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 41577.57
## 2 3a 41550.68
## 3 3b NA
## 4 3c 41549.80
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.149633 0.499594 -0.300 0.765
## phi -0.006973 0.015165 -0.460 0.646
## alpha 1.102278 0.068901 15.998 < 2e-16 ***
## A 679.844800 117.771389 5.773 8.57e-09 ***
## k 134.180867 20.797311 6.452 1.27e-10 ***
## p -0.012245 0.024633 -0.497 0.619
## s 1.254117 0.166550 7.530 6.59e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7544 on 3148 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 3.839e-06
## (24 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95131, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -16.973, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 130 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 130 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 622 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1954 1003.49
## 2 1953 928.39 1 75.104 157.9917 < 2.2e-16 ***
## 3 1937 895.74 16 32.646 4.4121 1.178e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24765.12
## 2 2 24614.88
## 3 3 24399.53
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.05559 0.59327 0.094 0.925
## phi 0.18837 0.01197 15.737 < 2e-16 ***
## alpha 0.71395 0.08936 7.990 2.29e-15 ***
## A 650.60407 109.71876 5.930 3.58e-09 ***
## k 149.00776 17.04266 8.743 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.68 on 1937 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.68e-06
## (21 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1937 895.74
## 2 1936 894.84 1 0.90602 1.9602 0.1617
## 3 1936 895.20 0 0.00000
## 4 1935 894.82 1 0.38442 0.8313 0.3620
## model AIC
## 1 3 24399.53
## 2 3a 24399.57
## 3 3b 24400.35
## 4 3c 24401.52
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.05559 0.59327 0.094 0.925
## phi 0.18837 0.01197 15.737 < 2e-16 ***
## alpha 0.71395 0.08936 7.990 2.29e-15 ***
## A 650.60407 109.71876 5.930 3.58e-09 ***
## k 149.00776 17.04266 8.743 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.68 on 1937 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.68e-06
## (21 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91719, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.1622, p-value = 0.001566
## alternative hypothesis: two.sided
## Warning in mean.default(G_M261$MEASTIM, na.rm = TE): argument is not numeric or
## logical: returning NA
## Warning: Removed 78 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 78 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1000 row(s) containing missing values (geom_path).
## Warning: Removed 20 rows containing missing values (geom_point).
## Warning: Removed 20 rows containing missing values (geom_pointrange).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 358 116.29
## 2 357 114.91 1 1.3849 4.3026 0.03877 *
## 3 356 109.97 1 4.9388 15.9884 7.752e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3786.810
## 2 2 3784.485
## 3 3 3770.626
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.91698 0.31202 -6.144 2.16e-09 ***
## phi 0.04519 0.02501 1.807 0.0716 .
## alpha 0.55854 0.12896 4.331 1.93e-05 ***
## A 784.22760 358.77095 2.186 0.0295 *
## k 309.03977 174.58871 1.770 0.0776 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5558 on 356 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 2.244e-06
## (1 observation deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 356 109.97
## 2 355 108.97 1 0.99453 3.2399 0.07271 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 3770.626
## 2 3a 3769.346
## 3 3b NA
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.92511 0.30822 -6.246 1.20e-09 ***
## phi 0.04613 0.02473 1.865 0.063 .
## alpha 0.56240 0.12712 4.424 1.29e-05 ***
## A 1370.33739 1598.54510 0.857 0.392
## k 723.17375 1016.90722 0.711 0.477
## p 0.02058 0.01912 1.076 0.283
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.554 on 355 degrees of freedom
##
## Number of iterations to convergence: 17
## Achieved convergence tolerance: 7.574e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94617, p-value = 3.48e-10
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.42121, p-value = 0.6736
## alternative hypothesis: two.sided
## Warning: Removed 12 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 12 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 112 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1693 593.44
## 2 1692 593.19 1 0.257 0.7328 0.3921
## 3 1691 541.23 1 51.954 162.3234 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 17724.61
## 2 2 17725.88
## 3 3 17572.42
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.04086 0.30450 -3.418 0.000645 ***
## phi 0.01372 0.01182 1.161 0.245733
## alpha 0.63633 0.04365 14.577 < 2e-16 ***
## A 282.79695 36.11588 7.830 8.53e-15 ***
## k 118.27243 12.83924 9.212 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5657 on 1691 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.307e-06
## (15 observations deleted due to missingness)
## Warning in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M331, : No starting values specified for some parameters.
## Initializing 'ge', 'phi', 'p', 'A', 's', 'k' to '1.'.
## Consider specifying 'start' or using a selfStart model
## Error in model.frame.default(formula = ~B_plt_t2_MgHa + MEASTIME_t2 + :
## variable lengths differ (found for '(sstart)')
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1691 541.23
## 2 1690 535.69 1 5.547 17.5 3.021e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 17572.42
## 2 3a 17556.95
## 3 3b 17566.65
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.037446 0.303163 -3.422 0.000636 ***
## phi 0.013711 0.011771 1.165 0.244266
## alpha 0.642684 0.042087 15.270 < 2e-16 ***
## A 362.891231 62.540663 5.802 7.79e-09 ***
## k 216.003260 50.875228 4.246 2.30e-05 ***
## p 0.048027 0.008704 5.518 3.96e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.563 on 1690 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.641e-06
## (15 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92789, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.6876, p-value = 1.289e-08
## alternative hypothesis: two.sided
## Warning: Removed 65 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 65 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 407 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2643 1183.5
## 2 2642 1180.0 1 3.523 7.8876 0.005014 **
## 3 2619 1115.4 23 64.675 6.6028 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 28925.26
## 2 2 28919.37
## 3 3 28591.03
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.74057 0.77386 0.957 0.33867
## phi 0.03712 0.01378 2.694 0.00711 **
## alpha 0.62727 0.05021 12.492 < 2e-16 ***
## A 199.15587 36.23088 5.497 4.24e-08 ***
## k 115.83174 10.56968 10.959 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6526 on 2619 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.738e-07
## (25 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2619 1115.4
## 2 2618 1104.2 1 11.112 26.344 3.066e-07 ***
## 3 2618 1112.9 0 0.000
## 4 2617 1080.5 1 32.414 78.508 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 28591.03
## 2 3a 28566.76
## 3 3b 28587.30
## 4 3c 28511.74
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) *
## A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.74782 0.76646 0.976 0.32931
## phi 0.03894 0.01345 2.896 0.00382 **
## alpha 0.62878 0.04666 13.475 < 2e-16 ***
## A 134.23475 24.50300 5.478 4.7e-08 ***
## k 79.39320 4.61436 17.206 < 2e-16 ***
## p 0.18835 0.01795 10.490 < 2e-16 ***
## s 2.52294 0.30264 8.336 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6426 on 2617 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 8.696e-06
## (25 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89951, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.7174, p-value = 2.389e-06
## alternative hypothesis: two.sided
## Warning: Removed 89 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 89 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 223 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1667 711.48
## 2 1666 709.28 1 2.201 5.1702 0.0231 *
## 3 1665 664.47 1 44.805 112.2688 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18878.73
## 2 2 18875.56
## 3 3 18768.58
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.31310 1.96054 1.180 0.23824
## phi 0.03559 0.01818 1.958 0.05039 .
## alpha 0.72328 0.06166 11.731 < 2e-16 ***
## A 245.20104 81.52998 3.007 0.00267 **
## k 174.51672 20.41966 8.547 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6317 on 1665 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.028e-06
## (5 observations deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1665 664.47
## 2 1664 664.44 1 0.036384 0.0911 0.7628
## model AIC
## 1 3 18768.58
## 2 3a 18770.49
## 3 3b NA
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.31310 1.96054 1.180 0.23824
## phi 0.03559 0.01818 1.958 0.05039 .
## alpha 0.72328 0.06166 11.731 < 2e-16 ***
## A 245.20104 81.52998 3.007 0.00267 **
## k 174.51672 20.41966 8.547 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6317 on 1665 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.028e-06
## (5 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93428, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.4397, p-value = 9.009e-06
## alternative hypothesis: two.sided
## Warning: Removed 65 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 65 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 140 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 358 148.13
## 2 357 146.78 1 1.348 3.2785 0.07103 .
## 3 356 127.34 1 19.443 54.3543 1.183e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3620.044
## 2 2 3618.744
## 3 3 3569.450
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.020903 0.487042 -2.096 0.03678 *
## phi 0.005339 0.031246 0.171 0.86442
## alpha 0.798409 0.093619 8.528 4.31e-16 ***
## A 148.459436 27.544549 5.390 1.29e-07 ***
## k 64.984251 20.289617 3.203 0.00148 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5981 on 356 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.243e-06
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 356 127.34
## 2 355 127.34 1 0.0016481 0.0046 0.9460
## 3 355 127.33 0 0.0000000
## 4 354 127.31 1 0.0237205 0.0660 0.7975
## model AIC
## 1 3 3569.450
## 2 3a 3571.445
## 3 3b 3571.418
## 4 3c 3573.351
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.020903 0.487042 -2.096 0.03678 *
## phi 0.005339 0.031246 0.171 0.86442
## alpha 0.798409 0.093619 8.528 4.31e-16 ***
## A 148.459436 27.544549 5.390 1.29e-07 ***
## k 64.984251 20.289617 3.203 0.00148 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5981 on 356 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.243e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94118, p-value = 9.029e-11
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.8532, p-value = 7.223e-12
## alternative hypothesis: two.sided
## Warning: Removed 13 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 13 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 53 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 209 70.054
## 2 208 70.043 1 0.0107 0.0319 0.8585
## 3 207 65.000 1 5.0433 16.0610 8.556e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2102.107
## 2 2 2104.074
## 3 3 2090.232
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.84715 0.39893 -4.630 6.44e-06 ***
## phi -0.03461 0.06344 -0.546 0.585921
## alpha 0.54693 0.11868 4.608 7.09e-06 ***
## A 251.83461 60.50467 4.162 4.62e-05 ***
## k 100.94261 28.20086 3.579 0.000429 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5604 on 207 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.946e-06
## (1 observation deleted due to missingness)
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 207 65.000
## 2 206 64.857 1 0.143 0.4542 0.5011
## model AIC
## 1 3 2090.232
## 2 3a 2091.765
## 3 3b 2092.003
## 4 3c NA
##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi *
## DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k +
## STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.84715 0.39893 -4.630 6.44e-06 ***
## phi -0.03461 0.06344 -0.546 0.585921
## alpha 0.54693 0.11868 4.608 7.09e-06 ***
## A 251.83461 60.50467 4.162 4.62e-05 ***
## k 100.94261 28.20086 3.579 0.000429 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5604 on 207 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.946e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93477, p-value = 3.981e-08
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.8139, p-value = 0.06969
## alternative hypothesis: two.sided
## Warning: Removed 9 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 9 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 102 row(s) containing missing values (geom_path).
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 3a |
| 212 | Laurentian Mixed Forest | 3a |
| 221 | Eastern Broadleaf Forest | 3b |
| 222 | Midwest Broadleaf Forest | 3a |
| 223 | Central Interior Broadleaf Forest | 3b |
| 231 | Southeastern Mixed Forest | 3c |
| 232 | Outer Coastal Plain Mixed Forest | 3c |
| 234 | Lower Mississippi Riverine Forest | 3a |
| 242 | Pacific Lowland Mixed Forest | NA |
| 251 | Prairie Parkland (Temperate) | 3b |
| 255 | Prairie Parkland (Subtropical) | 3b |
| 261 | California Coastal Chaparral Forest and Shrub | 1 |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | 3 |
| 313 | Colorado Plateau Semi-Desert | 1 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | 3 |
| 332 | Great Plains Steppe | 3 |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | 3a |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3b |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3c |
| M223 | Ozark Broadleaf Forest Meadow | 3 |
| M231 | Ouachita Mixed Forest | 3a |
| M242 | Cascade Mixed Forest | 3c |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 3 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 3a |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 3a |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3c |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3 |
| M334 | Black Hills Coniferous Forest | 3 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | 3 |
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | alpha | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6806 | 2847 | 0.4371575 | 0.0461307 | 0.8281844 | 0.0099476 | -0.0025514 | 0.0224466 | 0.8524407 | 0.7981315 | 0.9067499 | 468.94445 | 360.257205 | 577.63169 | 219.476246 | 145.923219 | 293.02927 |
| 212 | Laurentian Mixed Forest | east | 18775 | 8891 | 0.3065028 | 0.0938863 | 0.5191194 | -0.0014397 | -0.0086404 | 0.0057611 | 0.7214615 | 0.6787055 | 0.7642176 | 220.08251 | 200.844301 | 239.32071 | 112.272660 | 96.915095 | 127.63023 |
| 221 | Eastern Broadleaf Forest | east | 7170 | 3490 | 0.2301082 | -0.0225361 | 0.4827525 | -0.0036112 | -0.0126217 | 0.0053992 | 0.8410618 | 0.7885293 | 0.8935943 | 307.33549 | 264.280478 | 350.39050 | 68.630153 | 54.805106 | 82.45520 |
| 222 | Midwest Broadleaf Forest | east | 4877 | 2401 | -0.0867262 | -0.4859237 | 0.3124713 | 0.0210147 | 0.0022319 | 0.0397975 | 0.8854431 | 0.8026266 | 0.9682596 | 396.33948 | 313.733304 | 478.94566 | 150.640293 | 105.430043 | 195.85054 |
| 223 | Central Interior Broadleaf Forest | east | 8783 | 3725 | 0.2225534 | -0.0093636 | 0.4544704 | -0.0152826 | -0.0253331 | -0.0052322 | 0.7809661 | 0.7273449 | 0.8345873 | 181.12216 | 164.418748 | 197.82558 | 40.816766 | 35.581179 | 46.05235 |
| 231 | Southeastern Mixed Forest | east | 12347 | 5691 | 1.8230843 | 1.5213386 | 2.1248300 | -0.0126174 | -0.0211877 | -0.0040471 | 0.7248750 | 0.6970294 | 0.7527206 | 136.61080 | 127.848973 | 145.37264 | 32.316058 | 30.578266 | 34.05385 |
| 232 | Outer Coastal Plain Mixed Forest | east | 12470 | 6101 | 1.0902599 | 0.7956249 | 1.3848949 | 0.0146627 | 0.0037607 | 0.0255647 | 0.7472119 | 0.7172430 | 0.7771807 | 151.67548 | 140.028686 | 163.32228 | 35.068065 | 32.582439 | 37.55369 |
| 234 | Lower Mississippi Riverine Forest | east | 1265 | 714 | -0.0687997 | -0.8137570 | 0.6761576 | 0.0241647 | -0.0134990 | 0.0618284 | 0.7568143 | 0.6469309 | 0.8666977 | 914.88776 | -27.253358 | 1857.02888 | 324.181993 | -93.973657 | 742.33764 |
| 242 | Pacific Lowland Mixed Forest | pacific | 81 | 81 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 1797 | 809 | 0.2306491 | -0.4134437 | 0.8747419 | -0.0010402 | -0.0256571 | 0.0235767 | 0.7642603 | 0.6298616 | 0.8986590 | 149.64370 | 123.315855 | 175.97155 | 38.365093 | 32.472000 | 44.25819 |
| 255 | Prairie Parkland (Subtropical) | pacific | 663 | 293 | -0.1519659 | -0.9128520 | 0.6089201 | -0.0473764 | -0.0996120 | 0.0048592 | 0.8047939 | 0.6349630 | 0.9746248 | 122.71846 | 91.024638 | 154.41229 | 23.867545 | 16.909666 | 30.82542 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 24 | 24 | -2.7256829 | -3.4640155 | -1.9873504 | NA | NA | NA | NA | NA | NA | 8572.74879 | -10644.042016 | 27789.53960 | 717.133050 | -1012.557949 | 2446.82405 |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 155 | 155 | 0.4502648 | -2.6350178 | 3.5355473 | -0.0368603 | -0.1638641 | 0.0901435 | 0.9006637 | 0.4510901 | 1.3502372 | 1723.50465 | 233.267473 | 3213.74183 | 330.705756 | 140.032018 | 521.37949 |
| 313 | Colorado Plateau Semi-Desert | interior west | 215 | 215 | -0.9053040 | -2.7295824 | 0.9189744 | NA | NA | NA | NA | NA | NA | 293.73351 | 59.768000 | 527.69902 | 168.829282 | 22.480133 | 315.17843 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 304 | 240 | 5.5764039 | -6.5003964 | 17.6532042 | -0.1157279 | -0.1561570 | -0.0752988 | 0.4605733 | -0.0182672 | 0.9394138 | 35.68667 | -9.352018 | 80.72536 | 23.385902 | 4.496632 | 42.27517 |
| 332 | Great Plains Steppe | interior west | 195 | 106 | 0.3544169 | -3.2024025 | 3.9112362 | 0.0109591 | -0.0928977 | 0.1148159 | 0.7323201 | 0.1595394 | 1.3051009 | 280.40101 | -122.951818 | 683.75385 | 166.979849 | -110.571404 | 444.53110 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 62 | 62 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 121 | 120 | -1.0525367 | -4.8374009 | 2.7323276 | -0.0098922 | -0.1732311 | 0.1534468 | 0.5592955 | -0.0121371 | 1.1307280 | 68.81187 | -24.134919 | 161.75866 | -8.039455 | -10.657199 | -5.42171 |
| 411 | Everglades | east | 93 | 61 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6729 | 2989 | 0.4008521 | 0.1040018 | 0.6977023 | 0.0255848 | 0.0146118 | 0.0365578 | 0.8209380 | 0.7768288 | 0.8650472 | 244.84791 | 213.282676 | 276.41314 | 72.428643 | 59.016182 | 85.84110 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8034 | 3700 | 1.1056172 | 0.8450554 | 1.3661791 | -0.0404385 | -0.0484334 | -0.0324435 | 0.8455988 | 0.7838538 | 0.9073437 | 155.44566 | 146.677041 | 164.21428 | 38.721092 | 37.113658 | 40.32852 |
| M223 | Ozark Broadleaf Forest Meadow | east | 883 | 343 | -0.5924572 | -1.0317420 | -0.1531724 | 0.0766302 | 0.0413231 | 0.1119373 | 0.8907842 | 0.7511780 | 1.0303903 | 313.66069 | 243.751262 | 383.57012 | 90.944037 | 62.281589 | 119.60648 |
| M231 | Ouachita Mixed Forest | east | 988 | 481 | 0.4886076 | -0.5494169 | 1.5266321 | 0.0075901 | -0.0364130 | 0.0515932 | 0.7545905 | 0.5997496 | 0.9094315 | 367.93804 | 132.000820 | 603.87525 | 188.462564 | 21.433573 | 355.49155 |
| M242 | Cascade Mixed Forest | pacific | 3179 | 3176 | -0.1496328 | -1.1291959 | 0.8299303 | -0.0069729 | -0.0367080 | 0.0227623 | 1.1022779 | 0.9671816 | 1.2373742 | 679.84480 | 448.928334 | 910.76126 | 134.180868 | 93.403209 | 174.95853 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1963 | 1963 | 0.0555897 | -1.1079232 | 1.2191027 | 0.1883667 | 0.1648920 | 0.2118414 | 0.7139495 | 0.5387062 | 0.8891927 | 650.60407 | 435.424800 | 865.78334 | 149.007758 | 115.583882 | 182.43163 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 19 | 19 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 362 | 362 | -1.9251098 | -2.5312721 | -1.3189476 | 0.0461314 | -0.0025125 | 0.0947753 | 0.5624000 | 0.3123993 | 0.8124008 | 1370.33739 | -1773.471530 | 4514.14631 | 723.173749 | -1276.746049 | 2723.09355 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1711 | 1711 | -1.0374461 | -1.6320611 | -0.4428311 | 0.0137112 | -0.0093767 | 0.0367992 | 0.6426835 | 0.5601352 | 0.7252318 | 362.89123 | 240.225933 | 485.55653 | 216.003260 | 116.218180 | 315.78834 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2649 | 2648 | 0.7478240 | -0.7551014 | 2.2507495 | 0.0389391 | 0.0125700 | 0.0653082 | 0.6287834 | 0.5372856 | 0.7202812 | 134.23475 | 86.187536 | 182.28195 | 79.393196 | 70.345035 | 88.44136 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1675 | 1675 | 2.3131038 | -1.5322881 | 6.1584956 | 0.0355912 | -0.0000601 | 0.0712426 | 0.7232759 | 0.6023455 | 0.8442063 | 245.20104 | 85.288963 | 405.11312 | 174.516721 | 134.465815 | 214.56763 |
| M334 | Black Hills Coniferous Forest | interior west | 362 | 170 | -1.0209034 | -1.9787446 | -0.0630621 | 0.0053394 | -0.0561113 | 0.0667901 | 0.7984092 | 0.6142943 | 0.9825241 | 148.45944 | 94.288949 | 202.62992 | 64.984251 | 25.081675 | 104.88683 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 213 | 213 | -1.8471475 | -2.6336277 | -1.0606673 | -0.0346124 | -0.1596797 | 0.0904549 | 0.5469294 | 0.3129474 | 0.7809115 | 251.83461 | 132.550233 | 371.11899 | 100.942609 | 45.344890 | 156.54033 |
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
## Warning: Removed 10 rows containing missing values (geom_point).
## Warning: Removed 8 rows containing missing values (geom_point).
## region weighted.ge
## 1 entire US 0.5648211
## 2 pacific -0.0713743
## 3 east 0.6599584
## 4 interior west 0.5121994
## region weighted.phi
## 1 entire US 0.0087208848
## 2 pacific 0.0576288559
## 3 east -0.0003007545
## 4 interior west 0.0223131748
## region weighted.alpha
## 1 entire US 0.7725505
## 2 pacific 0.9272180
## 3 east 0.7789555
## 4 interior west 0.6202502
## region weighted.A
## 1 entire US 289.7046
## 2 pacific 693.1076
## 3 east 238.1320
## 4 interior west 0.0000
## region weighted.k
## 1 entire US 99.78948
## 2 pacific 139.51589
## 3 east 83.28670
## 4 interior west 162.11636